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Juliette [100K]
3 years ago
14

vector w has magnitude 25.0 and direction angle 41.7 degrees. Calculate the horizontal and vertical components of w

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
5 0

Consider the attached picture. It represents a vector, centered in the origin with angle 41.7 degrees, and a circumference with radius 25, centered in the origin.

As you can see, the horizontal and vertical components of the vector correspond to the lengths of segments OD and OC, respectively.

You might recognize this scenario from you trigonometry class: if the circle had radius 1, we would have

OD=\cos(41.7),\quad OC=\sin(41.7)

Since the circle has radius 25, we have to scale those coordinates:

OD=25\cos(41.7),\quad OC=25\sin(41.7)

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azamat

<h3>Answer:</h3>

Equation of the ellipse = 3x² + 5y² = 32

<h3>Step-by-step explanation:</h3>

<h2>Given:</h2>

  • The centre of the ellipse is at the origin and the X axis is the major axis

  • It passes through the points (-3, 1) and (2, -2)

<h2>To Find:</h2>

  • The equation of the ellipse

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  • a²b² = 9b² + a²

Multiply by 4 on both sides,

  • 4a²b² = 36b² + 4a²------(1)

Also by given the ellipse passes through the point (2, -2)

Substituting this,

\sf \dfrac{2^2}{a^2} +\dfrac{(-2)^2}{b^2} =1

Cross multiply,

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Subtracting equations 2 and 1,

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  • 3a² = 32
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Substituting in 2,

  • 32/3 × b² = 4b² + 4 × 32/3
  • 32/3 b² = 4b² + 128/3
  • 32/3 b² = (12b² + 128)/3
  • 32b² = 12b² + 128
  • 20b² = 128
  • b² = 128/20 = 32/5

Substituting the values in the equation for ellipse,

\sf \dfrac{x^2}{32/3} +\dfrac{y^2}{32/5} =1

\sf \dfrac{3x^2}{32} +\dfrac{5y^2}{32} =1

Multiplying whole equation by 32 we get,

3x² + 5y² = 32

<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>
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